Model description
The model is a sum of a pseudo-Voigt elastic peak (free mixing and FWHM), a Gaussian breathing phonon (free FWHM), a resolution-convolved DHO magnon, and a linear background:
Individual Components
1. Elastic Peak (Pseudo-Voigt, free mixing and FWHM)
where $\mu$ is the mixing parameter (free), $\text{FWHM}_1$ is free, and: - $L(E, x_1, \text{FWHM}_1) = \frac{(\text{FWHM}_1/2)^2}{(E - x_1)^2 + (\text{FWHM}_1/2)^2}$ (Lorentzian) - $G(E, x_1, \text{FWHM}_1) = \exp\left(-\frac{(E - x_1)^2}{2\sigma_1^2}\right)$ where $\sigma_1 = \frac{\text{FWHM}_1}{2\sqrt{2\ln(2)}}$ (Gaussian)
2. Breathing Mode (Gaussian, free FWHM)
where $\sigma_2 = \frac{\text{FWHM}_2}{2\sqrt{2\ln(2)}}$ and $\text{FWHM}_2$ is free
3. Magnon Peak (DHO convolved with fixed Gaussian resolution)
where $\gamma = \frac{FWHM_3}{2}$ (free parameter), and $G_{\text{res}}(E)$ is a Gaussian with FWHM = 0.044 eV (fixed resolution)
4. Linear Background
Fixed Parameters
- Magnon convolution resolution: FWHM = 0.044 eV
Free Parameters
- Elastic peak position: $x_1$
- Elastic peak amplitude: $A_1$
- Elastic peak FWHM: $\text{FWHM}_1$
- Elastic mixing parameter: $\mu$
- Breathing peak position: $x_2$
- Breathing peak amplitude: $A_2$
- Breathing peak FWHM: $\text{FWHM}_2$
- Magnon peak position: $x_3$
- Magnon peak amplitude: $A_3$
- Magnon FWHM: $\text{FWHM}_3$
- Background slope: slope
- Total: 11 free parameters